laurie,
I’m just tuning in here, so pardon me if I restate anything.
First off, you are using a self-hosted WordPress install, right? Not a myname.wordpress.com site?
If you are, log-in to your back-end at yoursitename.com/wp-admin using your name/pw. When the dashboard displays, it should show you stuff like “Right Now”, “Quick Press” “Recent Comments” etc. On the left you should have a vertical menu bar. It might be hidden, and just be a line of icons, in which case you can expand it by clicking the little arrow at the bottom.
Somewhere in the menu, around the middle or bottom, is a link for “Plugins” When you click that you will get a page displaying your currently installed plugins (even a stock install comes with two, Hello Dolly and Akismet). “Add New” is at the top (in up-to-date versions of WP, you can actually reach the add new through a fly-ou sub-menu).
The Add New link takes you to a screen where you can search plug-ins. You can either search TinyMCE here and choose which plugin you want to install. If you’ve downloaded it to your computer, you can click the link at the top “Upload” and use the file upload window to navigate to where the .zip is on your local computer.
When you click “Install Now” a screen will appear (very quickly for small plugins) that show your the progress. Once it’s installed, there will be a few options on under the report. “Activate Plugin” is one of them. Click that and it will be activated. You can also activate it from the main “Plugin” screen. Once activated, it should have some options or configuration screens. These can be just about anywhere in that vertical menu on the left, but generally are found under “Settings” or “Tools”. Not having ever used TinyMCE, I can’t really speak as to how it behaves from here, but this should get you off to a good start.
Let me know how this goes, and if it doesn’t work, where things go wrong for you.
Chris